As shown in figure an inductor of inductance 200, mH is connected to an AC source of emf 220 ,V and

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7.Alternating Current

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As shown in the figure an inductor of inductance $200\, mH$ is connected to an $AC$ source of emf $220 \,V$ and frequency $50 \,Hz$. The instantaneous voltage of the source is $0\, V$ when the peak value of current is $\frac{\sqrt{a}}{\pi} A$. The value of a is..........

A

$282$

B

$242$

C

$247$

D

$867$

(JEE MAIN-2022)

Solution

$f =50 Hz$

$X _{ L }=2 \pi fL$

$=2 \pi(50)\left(200 \times 10^{-3}\right)$

$=20 \pi \Omega$

$i _{0}=\frac{ V _{0}}{ X _{ L }} \Rightarrow \frac{ V _{ rms } \sqrt{2}}{ X _{ L }}$

$=\frac{(220) \sqrt{2}}{20 \pi}=\frac{11 \sqrt{2}}{\pi}$

$i _{ o }=\frac{\sqrt{242}}{\pi}$

Standard 12

Physics

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